Seismic velocity inversion drops its handcrafted prior: a diffusion model as projector cuts Marmousi MAE from 94.80 to 92.68
Synopsis
Full waveform inversion reconstructs subsurface velocity models from seismic records, but it is highly nonlinear and ill-posed, and an inaccurate initial model or noisy data can push it to a wrong solution. Bayesian full waveform inversion built on annealed Stein variational gradient descent previously constrained its particles with handcrafted Gaussian or smoothing priors that cannot represent complex geology. This work embeds a diffusion model trained on the GeoFWI dataset as an implicit geological projection operator inside the particle update, lowering mean absolute error on the Marmousi synthetic model from 94.80 with the classic method to 92.68, raising structural similarity from 0.69 to 0.72, and concentrating posterior uncertainty near deep structures and high-contrast interfaces.
Interpretation
Bayesian full waveform inversion can now guide particle evolution with geological structure learned from a velocity-model dataset, beyond the data likelihood, instead of relying on handcrafted Gaussian or smoothing priors. The earlier annealed Stein variational gradient descent full waveform inversion used only simple handcrafted priors, and with noise, limited illumination or incomplete data, likelihood-driven particle updates produced geologically inconsistent samples and inversion artifacts. On the Marmousi synthetic model, classic annealed Stein variational gradient descent and the diffusion-regularized version each used 50 particles and 100 iterations, giving mean absolute errors of 94.80 and 92.68, structural similarities of 0.69 and 0.72, and model signal-to-noise ratios of 21.19 dB and 21.48 dB.
The method treats a pretrained diffusion model as a geological projection operator that pushes particles toward the learned velocity-model distribution after each annealed Stein variational gradient update. The diffusion model is not used only for particle initialization or post-processing; it enters the particle update direction through shaping regularization, so particles are first corrected by the annealed Stein variational gradient and then projected as a whole through the diffusion model. The diffusion prior is trained on the GeoFWI dataset, which contains about 50,000 velocity models covering folds, faults and salt bodies on a 100 by 100 grid, with velocities from 1500 to 4500 m/s and 2 to 11 layers; inversion solves the acoustic wave equation with Deepwave under PyTorch.
Perspective
The demonstrated scope is acoustic full waveform inversion: the Marmousi and Overthrust synthetic models plus one field dataset acquired offshore China, the latter using 40 shots, band-pass filtered data between 5 and 15 Hz, and 30 iterations.
When noise is raised to a data signal-to-noise ratio of 2 dB, the posterior mean becomes less continuous and local perturbations increase in the deep region and near model boundaries; raising the particle count from 50 to 100 mainly stabilizes the uncertainty estimate, with limited improvement in the mean, while computation roughly doubles from about 20 minutes to 40 minutes. The starting timestep and patch shift of the diffusion regularization affect results, and the geological diversity of the training data strongly influences final performance.